Passive Scalar: Scaling Exponents and Realizability

An isotropic passive scalar field $T$ advected by a rapidly-varying velocity field is studied. The tail of the probability distribution $P(\theta,r)$ for the difference $\theta$ in $T$ across an inertial-range distance $r$ is found to be Gaussian. Scaling exponents of moments of $\theta$ increase as $\sqrt{n}$ or faster at large order $n$, if a mean dissipation conditioned on $\theta$ is a nondecreasing function of $|\theta|$. The $P(\theta,r)$ computed numerically under the so-called linear ansatz is found to be realizable. Some classes of gentle modifications of the linear ansatz are not realizable.Comment: Substantially revised to conform with published version. Revtex (4 pages) with 2 postscript figures. Send email to [email protected]

Multifractality and scale invariance in human heartbeat dynamics

Human heart rate is known to display complex fluctuations. Evidence of multifractality in heart rate fluctuations in healthy state has been reported [Ivanov et al., Nature {\bf 399}, 461 (1999)]. This multifractal character could be manifested as a dependence on scale or beat number of the probability density functions (PDFs) of the heart rate increments. On the other hand, scale invariance has been recently reported in a detrended analysis of healthy heart rate increments [Kiyono et al., Phys. Rev. Lett. {\bf 93}, 178103 (2004)]. In this paper, we resolve this paradox by clarifying that the scale invariance reported is actually exhibited by the PDFs of the sum of detrended healthy heartbeat intervals taken over different number of beats, and demonstrating that the PDFs of detrended healthy heart rate increments are scale dependent. Our work also establishes that this scale invariance is a general feature of human heartbeat dynamics, which is shared by heart rate fluctuations in both healthy and pathological states

Compositional redistribution during casting of Hg sub 0.8 Cd sub 0.2 Te alloys

A series of Hg(0.8)Cd(0.2)Te ingots was cast both vertically and horizontally under well-defined thermal conditions by using a two-zone furnace with isothermal heat-pipe liners. The main objective of the experiments was to establish correlations between casting parameters and compositional redistribution and to develop ground-based data for a proposed flight experiment of casting of Hg(1-x)Cd(x)Te alloys under reduced gravity conditions. The compositional variations along the axial and radial directions were determined by precision density measurements, infrared transmission spectra, and X-ray energy dispersion spectrometry. Comparison between the experimental results and a numerical simulation of the solidification process of Hg(0.8)Cd(0.2)Te is described

Active and Passive Fields in Turbulent Transport: the Role of Statistically Preserved Structures

We have recently proposed that the statistics of active fields (which affect the velocity field itself) in well-developed turbulence are also dominated by the Statistically Preserved Structures of auxiliary passive fields which are advected by the same velocity field. The Statistically Preserved Structures are eigenmodes of eigenvalue 1 of an appropriate propagator of the decaying (unforced) passive field, or equivalently, the zero modes of a related operator. In this paper we investigate further this surprising finding via two examples, one akin to turbulent convection in which the temperature is the active scalar, and the other akin to magneto-hydrodynamics in which the magnetic field is the active vector. In the first example, all the even correlation functions of the active and passive fields exhibit identical scaling behavior. The second example appears at first sight to be a counter-example: the statistical objects of the active and passive fields have entirely different scaling exponents. We demonstrate nevertheless that the Statistically Preserved Structures of the passive vector dominate again the statistics of the active field, except that due to a dynamical conservation law the amplitude of the leading zero mode cancels exactly. The active vector is then dominated by the sub-leading zero mode of the passive vector. Our work thus suggests that the statistical properties of active fields in turbulence can be understood with the same generality as those of passive fields.Comment: 13 pages, 13 figures, submitted to Phys. Rev.

Theory of Concentration Dependence in Drag Reduction by Polymers and of the MDR asymptote

A simple model of the effect of polymer concentration on the amount of drag reduction in turbulence is presented, simulated and analyzed. The qualitative phase diagram of drag coefficient vs. Reynolds number (Re) is recaptured in this model, including the theoretically elusive onset of drag reduction and the Maximum Drag Reduction (MDR) asymptote. The Re-dependent drag and the MDR are analytically explained, and the dependence of the amount of drag on material parameters is rationalized

High-temperature phase transitions in SrBi_2Ta_2O_9 film: a study by THz spectroscopy

Time-domain THz transmission experiment was performed on a $\rm SrBi_2Ta_2O_9$ film deposited on sapphire substrate. Temperatures between 300 and 923 K were investigated and complex permittivity spectra of the film were determined. The lowest frequency optic phonon near 28 cm$^{-1}$ reveals a slow monotonic decrease in frequency on heating with no significant anomaly near the phase transitions. We show that the dielectric anomaly near the ferroelectric phase transition can be explained by slowing down of a relaxational mode, observed in the THz spectra. A second harmonic generation signal observed in a single crystal confirms a loss of center of symmetry in the ferroelectric phase and a presence of polar clusters in the intermediate ferroelastic phase.Comment: subm. to J. Phys.: Condens. Matte

Unconventional Gravitational Excitation of a Schwarzschild Black Hole

Besides the well-known quasinormal modes, the gravitational spectrum of a Schwarzschild black hole also has a continuum part on the negative imaginary frequency axis. The latter is studied numerically for quadrupole waves. The results show unexpected striking behavior near the algebraically special frequency $\Omega=-4i$. This reveals a pair of unconventional damped modes very near $\Omega$, confirmed analytically.Comment: REVTeX4, 4pp, 6 EPS figure files. N.B.: "Alec" is my first, and "Maassen van den Brink" my family name. v2: better pole placement in Fig. 1. v3: fixed Refs. [9,20]. v4: added context on "area quantum" research; trimmed one Fig.; textual clarification

Probability Density Function of Longitudinal Velocity Increment in Homogeneous Turbulence

Two conditional averages for the longitudinal velocity increment u_r of the simulated turbulence are calculated: h(u_r) is the average of the increment of the longitudinal Laplacian velocity field with u_r fixed, while g(u_r) is the corresponding one of the square of the difference of the gradient of the velocity field. Based on the physical argument, we suggest the formulae for h and g, which are quite satisfactorily fitted to the 512^3 DNS data. The predicted PDF is characterized as (1) the Gaussian distribution for the small amplitudes, (2) the exponential distribution for the large ones, and (3) a prefactor before the exponential function for the intermediate ones.Comment: 4 pages, 4 figures, using RevTeX3.

Nonequilibrium spin transport on Au(111) surfaces

The well-known experimentally observed \textit{sp}-derived Au(111) Shockley surface states with Rashba spin splitting are perfectly fit by an effective tight-binding model, considering a two-dimensional hexagonal lattice with $p_{z}$-orbital and nearest neighbor hopping only. The extracted realistic band parameters are then imported to perform the Landauer-Keldysh formalism to calculate nonequilibrium spin transport in a two-terminal setup sandwiching a Au(111) surface channel. Obtained results show strong spin density on the Au(111) surface and demonstrate (i) intrinsic spin-Hall effect, (ii) current-induced spin polarization, and (iii) Rashba spin precession, all of which have been experimentally observed in semiconductor heterostructures, but not in metallic surface states. We therefore urge experiments in the latter for these spin phenomena.Comment: 5 pages, 3 figures, to be published in Phys. Rev.

Wave Propagation in Gravitational Systems: Completeness of Quasinormal Modes

The dynamics of relativistic stars and black holes are often studied in terms of the quasinormal modes (QNM's) of the Klein-Gordon (KG) equation with different effective potentials $V(x)$. In this paper we present a systematic study of the relation between the structure of the QNM's of the KG equation and the form of $V(x)$. In particular, we determine the requirements on $V(x)$ in order for the QNM's to form complete sets, and discuss in what sense they form complete sets. Among other implications, this study opens up the possibility of using QNM expansions to analyse the behavior of waves in relativistic systems, even for systems whose QNM's do {\it not} form a complete set. For such systems, we show that a complete set of QNM's can often be obtained by introducing an infinitesimal change in the effective potential